- #1

- 30

- 6

You are using an out of date browser. It may not display this or other websites correctly.

You should upgrade or use an alternative browser.

You should upgrade or use an alternative browser.

- I
- Thread starter JorgeM
- Start date

- #1

- 30

- 6

- #2

Science Advisor

- 3,182

- 1,538

Which integral?

- #3

- 320

- 108

$$ \zeta(s)=\frac{\Gamma(1-s)}{2 \pi i} \mathop\int_{\multimap} \frac{x^{s-1}}{e^{-x}-1}dx$$

Nevertheless, one of the most beautiful constructs in Mathematics IMO.

- #4

Science Advisor

Gold Member

- 3,297

- 682

I think that the Riemann zeta function is meromorphic in the entire complex plane with a single pole at 1 . It makes sense to takes its line integral along any piecewise smooth curve that goes not pass through the pole.

Share:

- Replies
- 3

- Views
- 400

- Replies
- 2

- Views
- 1K

- Replies
- 8

- Views
- 488

- Replies
- 3

- Views
- 960

- Replies
- 1

- Views
- 591

- Replies
- 14

- Views
- 1K

- Replies
- 5

- Views
- 378

- Replies
- 2

- Views
- 484

- Replies
- 0

- Views
- 1K

- Replies
- 2

- Views
- 589